I am VERY new to the Pen tool. After creating a path with the Pen tool, such as the one in the attached image, how can I go back and adjust the end of the path in the lower right corner? It is currently curling up, how can I adjust the curve of it, or maybe shorten the length of the path at this side?

In addition to what Steve said, you can effortlessly switch back and forth between adjusting the Handles (angles/lengths) and the position of the current Anchor Point with the Spacebar, which lets you drag the Anchor Point by the Handle.

This is used in most Adobe programs (in fact I don't know in which it is not). In Illustrator during creation of objects and paths, before releasing the mouse button, holding the space bar down and dragging moves the unfinished object or last anchor of the unfinished path. Releasing the space bar before releasing the mouse allows you to continue with completing the object or moving the handles of anchors after being repositioned. In other programs like Photoshop it doesn't work with anchor points but it works with creating objects (shapes) and certain selections and tools like the rectangular marquee and the crop tool.

On the Mac it's the space bar as well that lets you (temporarily) move an anchor point while dragging a handle with the Selection tool or Direct Selection tool.

This is news to me. I have always used the Cmd key for temporarily moving anchors and/or handles (works the same way in Photoshop). I just tried using the space bar on a handle but it only allows you to move the point and the handles with it. To adjust handles (like the OP asked about) it's the Cmd key and probably the Ctrl key on Windows. This temporarily calls up the direct selection tool as long as you hit the A key prior to drawing with the pen.

... have always used the Cmd key for temporarily moving anchors and/or handles (works the same way in Photoshop). I just tried using the space bar on a handle but it only allows you to move the point and the handles with it...

The main difference is that with the space bar you don't make additional clicks, switch tools, and it allows you to reposition an anchor during dragging a handle. Also with the space bar you can reposition the first (starting) point of a path before releasing the mouse and then continue with completing the path which is not possible with the Ctrl/Cmd. Reposition the first point with space bar during path creation is very helpful when you want to start a new path at the ends of another path - to avoid adding to the existing path, first you have to click away from the end points and then move (snap) the first anchor of the new path there.

Ctrl/Cmd is good when you want to change the position of an anchor after releasing the mouse because the space bar function doesn't work after the mouse button is released, otherwise the space bar is less effort.